Finite analogues of Euclidean space

JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS

卷:68

Article

Medrano, A ; Myers, P ; Stark, HM ; Terras, A

关键词: finite symmetric space;    Ramanujan graph;    Kloosterman sum;   

DOI  :  10.1016/0377-0427(95)00261-8

来源: Elsevier

【 摘 要 】

Graphs are attached to F-q(n), where F-q is the field with q elements, q odd, using an analogue of the Euclidean distance. The graphs are shown to be asymptotically Ramanujan for large q (better than Ramanujan in half the cases). Comparisons are made with finite upper half planes constructed in a similar way using an analogue of Poincare's non-Euclidean distance. The eigenvalues of the adjacency operators of the finite Euclidean graphs are shown to be Kloosterman sums.

【 授权许可】

Free